The Garden of Eden theorem: old and new

Abstract

We review topics in the theory of cellular automata and dynamical systems that are related to the Moore-Myhill Garden of Eden theorem.

This is a further updated version; it includes an INDEX. To appear in Handbook of Group Actions, (ed. L. Ji, A. Papadopoulos and S.T. Yau), Vol. V, International Press and Higher Education Press, 2018

References in corpus (3)

• Amenability of groups is characterized by Myhill's Theorem
• Cellular automata on a $G$-set
• A Garden of Eden theorem for principal algebraic actions

Cited by in corpus (3)

• On sofic groups, Kaplansky's conjectures, and endomorphisms of pro-algebraic groups
• Garden of Eden and Specification
• On the Garden of Eden theorem for B-free subshifts